# Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 44, Issue: 3, page 313-337
- ISSN: 0988-3754

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topTurek, Ondřej. "Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words." RAIRO - Theoretical Informatics and Applications 44.3 (2010): 313-337. <http://eudml.org/doc/250799>.

@article{Turek2010,

abstract = {
A word u defined over an alphabet $\mathcal A$ is c-balanced (c∈$\mathbb N$) if for all pairs of factors v, w of u of the same length
and for all letters a∈$\mathcal A$, the difference between the number of letters a in v and w is less or equal to c. In this paper we consider a ternary alphabet
$\mathcal A$ = \{L, S, M\} and a class of substitutions $\varphi_p$ defined by $\varphi_p$(L) = LpS, $\varphi_p$(S) = M,
$\varphi_p$(M) = Lp–1S where p> 1.
We prove that the fixed point of $\varphi_p$, formally written as $\varphi_p^\infty$(L), is 3-balanced and that its Abelian complexity is bounded above by the value 7, regardless of the value of p. We also show that both these bounds are optimal, i.e. they cannot be improved.
},

author = {Turek, Ondřej},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Balance property; Abelian complexity; substitution; ternary word; balance property},

language = {eng},

month = {10},

number = {3},

pages = {313-337},

publisher = {EDP Sciences},

title = {Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words},

url = {http://eudml.org/doc/250799},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Turek, Ondřej

TI - Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/10//

PB - EDP Sciences

VL - 44

IS - 3

SP - 313

EP - 337

AB -
A word u defined over an alphabet $\mathcal A$ is c-balanced (c∈$\mathbb N$) if for all pairs of factors v, w of u of the same length
and for all letters a∈$\mathcal A$, the difference between the number of letters a in v and w is less or equal to c. In this paper we consider a ternary alphabet
$\mathcal A$ = {L, S, M} and a class of substitutions $\varphi_p$ defined by $\varphi_p$(L) = LpS, $\varphi_p$(S) = M,
$\varphi_p$(M) = Lp–1S where p> 1.
We prove that the fixed point of $\varphi_p$, formally written as $\varphi_p^\infty$(L), is 3-balanced and that its Abelian complexity is bounded above by the value 7, regardless of the value of p. We also show that both these bounds are optimal, i.e. they cannot be improved.

LA - eng

KW - Balance property; Abelian complexity; substitution; ternary word; balance property

UR - http://eudml.org/doc/250799

ER -

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